Two gears are connected and are rotating simultaneously. the smaller gear has a radius of 3 inches, and the larger gear has a radius of 7 inches. part 1: what is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation? part 2: how many rotations will the smaller gear make during one complete rotation of the larger gear?

Part 1: Angle = 154.3°

Part 2: About 2.33 Rotations

Step-by-step explanation:

Part 1:

The arc length of a circle is given by the formula  

Where

**The angle are in radians and we will use radian**

When smaller gear has made 1 complete rotations ( radians), the arc length traveled is

Now, what angle is swept by the larger circle when it travels ? Put in and r is 7 to find :

** Since radians is 180°, we plug in 180 into and find the degree measure:

Angle = 154.3°

Part 2:

In one complete rotation of the larger gear, it travels a distance of:

We know that the smaller circle makes 1 rotation and travels , so in distance, it makes:

Rotations =

About 2.33 Rotations

20

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